Known variable speed drive units include hydrostatic drives, viscous drives, toroidal drives, and Vari-Cool™ and similar variable sheave drives. Variable sheave designs use the side of the belt and axial force to affect different speed ratios. The axial force pinches the belt which must be physically pulled out from the sheave pair. Certain belt drive power transmissions use a ribbed belt which has lengthwise grooves and which engages a pulley with grooves. Typically, the pulleys in such a rib-belt drive have a fixed radius, and thus, have a fixed ratio between the radius of the driving pulley and the radius of the driven pulley. It is desired to provide a variable radius pulley for such a ribbed belt drive which has the efficiency of a typical poly-rib belt drive.